Motor with variable angular speed

I am interested in the fllowing issue and I would appreciate any help:
I need a motor that has a variable angular speed. To be more exact: the angular speed needs to be a f(1/sin(theta)) where theta is the angle of rotation varying between 1 to 89 degrees.
Does anyone know if this type of motor exist in the market? or: does anyone know how could I build it myself?
Thank you in advance.

i would guess what you need to do is to measure the angle that the motor shaft is at (using a potentiometer) and then come up with some circutry which would take the voltage reading from the potentiometer and convert it to the voltage you need to have across the motor terminals to achiever the speed you want. or if you didnt want to build circutry you could plug the poteniometer output into some sort of data aquisition card and then write a programme to ouptut a voltage on the aquisitoion card and then wire your motor to this output.
anyhoo i dont know if this is any help. i've never done nething like it!